Question

the first term of a geometric series is -1, and the common ratio is -3. how many terms are in the series if its sum is 182?

Answer 1

hi :)

Answer 2

do you recall the formula for the sum of a geo series?

Answer 3

no ):

Answer 4

\[S=a_1\frac{1-r^n}{1-r}\]
solve for n
\[S\frac{1-r}{a_1}=1-r^n\]
\[S\frac{1-r}{a_1}-1=-r^n\]
\[S\frac{r-1}{a_1}+1=r^n\]which becomes a log i bleive

Answer 5

\[ln(S\frac{r-1}{a_1}+1)=ln(r^n)\]
\[ln(S\frac{r-1}{a_1}+1)=n ln(r)\]
\[\frac{ln(S\frac{r-1}{a_1}+1)}{ln~r}=n\]

Answer 6

thnx

Answer 7

yep, now its just a matter of filling in the values you are given and voila!! :)